Phase-Field Simulation of Microstructure Formation in Gas-Atomized Al–Cu–Li–Mg Powders

Al–Cu–Li (2xxx series) powders for additive manufacturing processes are often produced by gas atomization, a rapid solidification process. The microstructural evolution of gas-atomized powder particles during solidification was investigated by phase-field simulations using the software tool MICRESS. The following topics were investigated: (1) the microsegregation of copper and lithium in the particle, and the impact of lithium addition on the formation of secondary phases in Al-2.63Cu and Al-2.63Cu-1.56Li systems, (2) the effect of magnesium on the nucleation and final mass fraction of T1 (Al2CuLi) growing from the melt, and (3) the effect of increased magnesium content on the T1 and Sʹ (AlCu2Mg) phase fractions. It is observed that the addition of lithium into the Al–Cu system leads to a decrease in the solid solubility of copper in the primary matrix; consequently, more copper atoms segregate in the interdendritic regions resulting in a greater mass fraction of secondary precipitates. Our result agrees with findings on the beneficial impact of magnesium on the nucleation and precipitation kinetics of T1 precipitates in the conventional casting process with further thermomechanical heat treatments. Moreover, it is observed that the increase in magnesium from 0.28 wt.% to 0.35 wt.% does not significantly affect the nucleation and the amount of the T1 phase, whereas a decrease in T1 phase fraction and a delay of T1 formation are encountered when magnesium content is further raised to 0.49 wt.%.


Introduction
Low-density, high-strength materials provide a high specific strength which is of great interest and ideal for engineering and structural applications. Pure aluminum (99% or higher) 1xxx series is a material relatively soft because of its atomic structure-a closedpacked FCC lattice with high stacking fault energy and a large number of slip systems which allows dislocation slipping even at low temperatures and does not display ductile to brittle transition property [1]. Therefore, with the help of alloying elements, many aluminum alloys have been developed with improved strength, density, etc., for structural applications.
Aluminum-lithium alloys [2][3][4][5] are well-known in the aerospace industry because of their high strength and lightweight properties. As the light metal lithium with the lowest density of the elements under stable standard conditions, the addition of lithium to aluminum alloys is advantageous. Each 1 wt.% up to 4 wt.% addition of lithium leads to a reduction in the density by 3% and an increase in the elastic modulus by approximately Phase-field modeling [26] is a tool to simulate the microstructure evolution, including microsegregation in a spatially and temporally resolved manner. It considers the thermal process history and is thus not bound to a global equilibrium constraint, i.e., it only assumes local equilibrium at the phase boundaries. By this, fast solidification processes can also be simulated. Phase-field modeling is more general compared with a Scheil-Gulliver calculation and includes the option to consider nucleation undercooling and kinetic effects or diffusion-limited growth kinetic. When linked to thermodynamic databases, phase-field models lead to quantitative predictions for the phase fractions and the spatial distribution of alloying elements. Therefore, they have a wide range of applications, e.g., simulation of phase transformations [27], heat treatments [28,29], gas atomization [30], additive manufacturing [31,32], and many more. A recent formulation of a multicomponent/multiphase field model, as it is, for instance, implemented in the software MICRESS, is given in the reference [33]. Phase-field models are also applicable for fast solidification, as shown in the references [34,35]. The link between the microstructure evolution governed by the phase field and diffusion equations and the temperature evolution based on the energy balance is described in more detail in [36].
Several investigations have been carried out by different authors focusing on the cooling rate estimation of gas-atomized Al-Cu powders using the dendrite arm spacing (DAS) measurement [37], microsegregation of Al-Cu alloy under different cooling rates using two-dimensional (2-D) pseudo-front tracking (PFT) model [38], and many more. No work has been carried out in the ternary system where Li is added into Al-Cu alloy, especially alloying element distribution and secondary phase formation in the field of droplet solidification using phase-field simulation. Understanding the microsegregation of Cu and Li together with nucleation and formation of secondary phases during solidification is important for subsequent process steps, such as heat treatment, as microsegregation affects the solid-state precipitation of T 1 , which contributes to strengthening mechanisms in Al-Cu-Li alloys. The aim of this phase-field simulation study was to investigate the solidification behavior of a gas-atomized droplet, including the formation of secondary phases, especially T 1 , with a special focus on the microsegregation of the light element Li. Experimentally, the Li distribution is difficult to measure as standard EDX-detectors cannot detect Li because of its low energy characteristics. Hence, a quantitative phase-field model has been applied with the further advantage of a higher spatial resolution compared with an SEM-EDX analysis of a single atomized droplet. The cooling curve, solidification path, the mass fraction of secondary phases, and the segregation of the alloying elements Cu and Li are analyzed and quantified by the phase-field simulations. The effect of adding lithium on the microsegregation of copper and secondary phase fraction is investigated by comparing Al-2.63Cu and Al-2.63Cu-1.56Li powders. In addition, various magnesium contents were added to Al-2.63Cu-1.56Li to study its impact on the T 1 nucleation and phase fraction. Furthermore, simulation results were compared with results from the literature, and our own experimental results were compared with a commercially purchased Al-Cu-Li-Mg powder.

Material
In this study, commercially purchased gas-atomized Al-Cu-Li-Mg powder from Nanonval GmbH (Berlin, Germany) was used for the purpose of validating the simulation results. The nominal composition of the powder is listed in Table 1. In this paper, the phase-field simulation of the gas-atomized powder was performed using MICRESS software (Version 6.303, ACCESS e.V., Aachen, Germany) [39]. The simulations for the binary alloy Al-2.63Cu considered two solid phases, primary FCC_Al and θ (Al 2 Cu). Subsequently, the model was extended to multicomponent alloy systems with lithium and magnesium. For the alloy Al-2.63Cu-1.56Li, the formation of three solid phases, such as primary FCC_Al, T 1 , and T B (Al 7.5 Cu 4 Li), were taken into consideration. The droplet solidification of the alloy Al-2.63Cu-1.56Li-xMg comprises the formation of FCC_Al, T 1 , and S . In the phase-field simulation scenario, only the cooling process was considered since the aim of the present study was to understand the microsegregation and phase formation in the solidifying droplet. Table 2 summarizes the input parameters that were used in the droplet solidification model of gas-atomized powder. The initial concentrations of the alloying elements, i.e., copper, lithium, and magnesium, used in different simulations of Al-Cu, Al-Cu-Li, and Al-Cu-Li-Mg are described in Table 3.  It was required to define the phase interaction between the liquid and all solid phases, the primary FCC phase, and all other secondary phases, e.g., T 1 , T B , and S phase, in order to enable the growth or shrinkage of one phase at the expense of the other. The main condition for the nucleation of secondary phases from the melt was a critical nucleation undercooling, set to 3K for all secondary phases in all simulations. In addition, a nucleation temperature range, i.e., the minimum and maximum temperature, was defined for each desired second phase in which the precipitation of these second phases was expected. The nucleation ranges for the secondary precipitates in this model were taken from Thermocalc Scheil calculation; 750 and 821 • C for θ in Al-2.63Cu, 730 and 813 • C, 730 and 798 • C for T 1 and T B , respectively, in Al-2.63Cu-1.56Li, and 700 and 786 • C for S phase in Al-2.63Cu-1.56Li-0.28Mg. The maximum number of possible nuclei was not limited, but a minimal distance (shield distance) of 1µm was introduced to avoid the growth of new nuclei of the same phase around the initial nucleus due to the release of latent heat.
The grid spacing was set to ∆x = 0.02 µm, which was a compromise between resolution and calculation time in such a way that changes in grid spacing no longer significantly affected the simulation results. A two-dimensional simulation domain (circle shaped) was used instead of a three-dimensional spherical model as it offers results with sufficient accuracy, e.g., high spatial resolution with reasonably short calculation times. Only a quarter of a circle was used for simulation because of the symmetrical characteristic of the droplet, as demonstrated in Figure 1. There were a total of 504 cells in the X and Z directions, and the number of cells in the Y direction was set to 1 as it is a 2D simulation. The thickness of the diffuse interface was set to 0.08 µm (four grid cells). The grid spacing was set to ∆x = 0.02 μm, which was a compromise between resolu tion and calculation time in such a way that changes in grid spacing no longer significantly affected the simulation results. A two-dimensional simulation domain (circle shaped) wa used instead of a three-dimensional spherical model as it offers results with sufficient ac curacy, e.g., high spatial resolution with reasonably short calculation times. Only a quarte of a circle was used for simulation because of the symmetrical characteristic of the droplet as demonstrated in Figure 1. There were a total of 504 cells in the X and Z directions, and the number of cells in the Y direction was set to 1 as it is a 2D simulation. The thickness o the diffuse interface was set to 0.08 μm (four grid cells). The phase-field equation was solved together with an energy balance equation fo the temperature evolution and diffusion equations for the concentration field of the solut atoms. The phase-field model, i.e., the computation of driving forces for interface motion and nucleation and solute partitioning at the moving solid-liquid interfaces, was linked The phase-field equation was solved together with an energy balance equation for the temperature evolution and diffusion equations for the concentration field of the solute atoms. The phase-field model, i.e., the computation of driving forces for interface motion and nucleation and solute partitioning at the moving solid-liquid interfaces, was linked to the thermodynamic database TTAl8. The mobility database MOBAL1 along with the thermodynamic database was used to compute the diffusion coefficients of solute atoms in the liquid and primary solid FCC phases. The diffusion coefficient values described in Table 2 represent global equilibrium values which are temperature-and compositiondependent in the specific phases.

Initial Concentration
In this simulation scenario, the temperature evolution and, thus, the cooling rate were determined from the energy balance between external cooling, heat capacity, and latent heat. The cooling of the droplet was determined by a heat extraction rate (HER) (J/s*cm 2 ) as a measure of the heat transfer from the droplet to the surrounding inert gas by convection and radiation. However, the contribution of heat loss caused by radiation was very small, while convection was mainly responsible for droplet solidification. The thermal gradient was neglected as it was assumed that heat conductivity within the droplet is fast.

Approach
This research focused on the formation of eutectic fractions and microsegregation of alloying elements during the solidification of gas-atomized powder particles. A fast cooling rate was achieved when the liquid droplet was exposed to the inert gas in the atomization chamber. Consequently, mixing and redistributing alloying elements may differ from conventional casting with lower cooling rates, and the eutectic fraction may vary due to lower nucleation temperatures of the secondary phase.
In this research, the droplet solidification of Al-2.63Cu during gas atomization was simulated first, and then it was extended to Al-2.63Cu-1.56Li and Al-2.63Cu-1.56Li-0.28Mg. In addition, the magnesium content was varied in Al-2.63Cu-1.56Li-xMg. The comparison was made between Al-2.63Cu and Al-2.63Cu-1.56Li alloy solidification in terms of the cooling curve, solidification path, eutectic fraction, and segregation of copper atoms during solidification. Then, the influence of magnesium on the T 1 phase precipitation was studied. The last investigation was carried out to observe how varying magnesium contents in the quaternary alloy affects the mass fraction of the T 1 and S phase.

Phase Field Simulation
The precipitation sequence of Al-Cu-Li alloys exhibited features of both binary Al-Cu and Al-Li systems [11]. In Al-Cu, it was accompanied by the formation of θ precipitates and δ (Al 3 Li) phase in binary Al-Li alloys. However, T 1 was the major strengthening precipitate in Al-Cu-Li alloys. Its formation, particularly solid-state precipitation, depended on many factors such as Cu/Li ratio, minor alloying elements, or prior deformation by cold working. Therefore, to design an optimal heat treatment process, it was important to understand the nucleation and growth of all Cu-and Li-containing phases already nucleating from the melt along the solidification path, particularly in rapid solidification processing.
The simulated cooling curve for the heat extraction rate given in Table 2 and the corresponding solid fraction formation of both Al-2.63Cu and Al-2.63Cu-1.56Li are presented in Figure 2a,b, respectively. It can be seen in Figure 2a that addition of 1.56 wt.% of lithium into Al-2.63Cu led only to a slight decrease in the onset of solidification by nucleation of the primary FCC phase from 920 • C to 918 • C. The eutectic reaction also started at a lower temperature, 805 • C for Al-2.63Cu-1.56Li, compared with 815 • C for Al-2.63Cu. Additionally, the total amount of secondary phases in Al-2.63Cu-1.56Li was increased from approximately 2 to 2.5 wt.% compared with Al-2.63Cu, as shown in Figure 3a. There was only one secondary phase, θ (Al 2 Cu), in Al-2.63Cu, whereas two secondary phases were formed in Al-2.63Cu-1.56Li alloy, namely T 1 and T B (see Figure 3b). The decrease in nucleation temperature of the secondary phases when adding Li to the binary Al-2.63Cu can be seen directly in Figure 3b. formed in Al-2.63Cu-1.56Li alloy, namely T1 and TB (see Figure 3b). The decrease in nucleation temperature of the secondary phases when adding Li to the binary Al-2.63Cu can be seen directly in Figure 3b.    Huang and Zheng [9] reported that for conventional casting with additional aging treatment, θʹ phase formation is observed to be less frequent in the range of Li concentration from 0.5 wt.% to 1.6 wt.% and is entirely suppressed at a high Li level of 1.6 wt.%. In order to verify the effect of lithium concentration on secondary phase formation during rapid solidification, Scheil calculations were carried out, and the results are presented in Figure 4. According to the Scheil results, it may be concluded that θʹ formation can be expected when the lithium content is lower than 0.5 wt.%; above this, the θʹ formation is compensated by TB and T1 formation during rapid solidification. Huang and Zheng [9] reported that for conventional casting with additional aging treatment, θ phase formation is observed to be less frequent in the range of Li concentration from 0.5 wt.% to 1.6 wt.% and is entirely suppressed at a high Li level of 1.6 wt.%. In order to verify the effect of lithium concentration on secondary phase formation during rapid solidification, Scheil calculations were carried out, and the results are presented in Figure 4. According to the Scheil results, it may be concluded that θ formation can be expected when the lithium content is lower than 0.5 wt.%; above this, the θ formation is compensated by T B and T 1 formation during rapid solidification.  During solidification, the partitioning of lithium, copper, and other alloying elements at the growing solid-liquid interface leads to an inhomogeneous element distribution in the solidified particle. Post-heat treatment, such as homogenization, can eliminate these microsegregation effects [40]. However, the general understanding of the segregation in the as-solidified material is important for the adjustment of subsequent processing steps.
As an example, Al-Cu with different copper contents was simulated. The copper pileup ahead of the interface increased with increasing Cu concentration in the alloy, see  During solidification, the partitioning of lithium, copper, and other alloying elements at the growing solid-liquid interface leads to an inhomogeneous element distribution in the solidified particle. Post-heat treatment, such as homogenization, can eliminate these microsegregation effects [40]. However, the general understanding of the segregation in the as-solidified material is important for the adjustment of subsequent processing steps.
As an example, Al-Cu with different copper contents was simulated. The copper pileup ahead of the interface increased with increasing Cu concentration in the alloy, see  Figure 5e gives a sorted representation of the Cu concentration per computation grid cell, a common method to analyze the microsegregation [41,42]. In the simulation settings, the position of the FCC nucleus is predefined in the lower left corner of the simulation domain to respect the symmetry. In reality, nucleation is expected to take place at the surface rather than in the center. However, for a statistical investigation of the segregation, the position was not that relevant; more important were the length scales, i.e., dendrite arm spacing and cooling rate. As it is later discussed, the length scales of the simulation and experiment are comparable. The outward-growing dendrite leads to a Cu accumulation between the main branches (interdendritic region) and at the particle surface, which then exhibits the eutectic areas. In Figure 5e, the graph shows that copper concentration dissolves in the primary FCC matrix in Al-1.5Cu is 0.3 wt.%. It further increases to 0.5 wt.% and 0.8 wt.% with increasing nominal copper content in Al-2.63Cu and Al-4.5Cu, respectively. In Figure 6, a comparison between Al-2.63Cu and Al-2.63Cu-1.56Li is shown. The addition of Li as a second alloying element affected the partitioning of Cu at the solidification front, i.e., the effective distribution coefficient for Cu, c Cu sol/c Cu liq, is smaller, and the amount of copper dissolved in the primary FCC phase has dropped from approximately 0.5 wt.% to 0.3 wt.%. Consequently, the amount of copper pushed into the remaining liquid was larger for the Al-2.63Cu-1.56Li alloy compared with Al-2.63Cu, which led to a higher amount of secondary phases, i.e., fraction eutectic. In Figure 6, a comparison between Al-2.63Cu and Al-2.63Cu-1.56Li is shown. The addition of Li as a second alloying element affected the partitioning of Cu at the solidification front, i.e., the effective distribution coefficient for Cu, c Cu sol /c Cu liq , is smaller, and the amount of copper dissolved in the primary FCC phase has dropped from approximately 0.5 wt.% to 0.3 wt.%. Consequently, the amount of copper pushed into the remaining liquid was larger for the Al-2.63Cu-1.56Li alloy compared with Al-2.63Cu, which led to a higher amount of secondary phases, i.e., fraction eutectic.
addition of Li as a second alloying element affected the partitioning of Cu at the solidification front, i.e., the effective distribution coefficient for Cu, c Cu sol/c Cu liq, is smaller, and the amount of copper dissolved in the primary FCC phase has dropped from approximately 0.5 wt.% to 0.3 wt.%. Consequently, the amount of copper pushed into the remaining liquid was larger for the Al-2.63Cu-1.56Li alloy compared with Al-2.63Cu, which led to a higher amount of secondary phases, i.e., fraction eutectic. The image in Figure 7 shows the local Cu composition in the completely solidified powder particle. The segregation analysis in Figure 7b confirms a higher Cu concentration in the FCC phase in the binary alloy Al-2.63Cu compared with the ternary Al-2.63Cu-1.56Li alloy, although the nominal Cu concentration was the same for both alloys. It is reported The image in Figure 7 shows the local Cu composition in the completely solidified powder particle. The segregation analysis in Figure 7b confirms a higher Cu concentration in the FCC phase in the binary alloy Al-2.63Cu compared with the ternary Al-2.63Cu-1.56Li alloy, although the nominal Cu concentration was the same for both alloys. It is reported that the solid solubility of copper decreased when lithium atoms were added [7]. Consequently, there is a larger amount of copper available for the formation of secondary phases. that the solid solubility of copper decreased when lithium atoms were added [7]. Consequently, there is a larger amount of copper available for the formation of secondary phases. The segregation of lithium in Al-2.63Cu-1.56Li followed the same trend as Cu, but the segregation was not as strong. Approximately 1.3 wt.% of Li was dissolved in the FCC matrix, as represented in Figure 8. The segregated copper together with lithium led to the formation of ternary phases, such as T1 (Al2CuLi) and TB (Al15Cu8Li2), in the interdendritic regions. In Al-2.63Cu, the amount of copper needed to form θʹ in the interdendritic areas was larger. Therefore, the fraction of secondary phases was smaller, as shown in Figure 3a.
When taking a closer look at the concentration gradient of lithium atoms in Figure  8a, a depletion of lithium (dark blue spots) can be found between the secondary phases in the interdendritic regions and the FCC matrix. The segregation of lithium in Al-2.63Cu-1.56Li followed the same trend as Cu, but the segregation was not as strong. Approximately 1.3 wt.% of Li was dissolved in the FCC matrix, as represented in Figure 8. The segregated copper together with lithium led to the formation of ternary phases, such as T 1 (Al 2 CuLi) and T B (Al 15 Cu 8 Li 2 ), in the interdendritic regions. In Al-2.63Cu, the amount of copper needed to form θ in the interdendritic areas was larger. Therefore, the fraction of secondary phases was smaller, as shown in Figure 3a. trix, as represented in Figure 8. The segregated copper together with lithium led to the formation of ternary phases, such as T1 (Al2CuLi) and TB (Al15Cu8Li2), in the interdendritic regions. In Al-2.63Cu, the amount of copper needed to form θʹ in the interdendritic areas was larger. Therefore, the fraction of secondary phases was smaller, as shown in Figure 3a.
When taking a closer look at the concentration gradient of lithium atoms in Figure  8a, a depletion of lithium (dark blue spots) can be found between the secondary phases in the interdendritic regions and the FCC matrix. During solidification, T1, TB, and Sʹ precipitates grow partially out of the melt. For the solid-state precipitation of T1 at lower temperatures, a significant influence of magnesium is known from conventionally produced Al-Cu-Li alloys. It is reported in reference [12] that T1 precipitates heterogeneously and nucleates on dislocations and grain boundaries, and the addition of Mg and Ag leads to a uniform dispersion of T1 plates in the matrix of the conventionally produced Al-Cu-Li alloys. Moreover, it is expected that the addition of Mg to Al-Cu-Li alloys either favors the T1 nucleation or promotes the formation of the Sʹ phase, which belongs to the ternary Al-Cu-Mg system (see Scheil calculation in Figure 9). When taking a closer look at the concentration gradient of lithium atoms in Figure 8a, a depletion of lithium (dark blue spots) can be found between the secondary phases in the interdendritic regions and the FCC matrix.
3.1.2. Al-2.63Cu-1.56Li and Al-2.63Cu-1.56Li-0.28Mg During solidification, T 1 , T B , and S precipitates grow partially out of the melt. For the solid-state precipitation of T 1 at lower temperatures, a significant influence of magnesium is known from conventionally produced Al-Cu-Li alloys. It is reported in reference [12] that T 1 precipitates heterogeneously and nucleates on dislocations and grain boundaries, and the addition of Mg and Ag leads to a uniform dispersion of T 1 plates in the matrix of the conventionally produced Al-Cu-Li alloys. Moreover, it is expected that the addition of Mg to Al-Cu-Li alloys either favors the T 1 nucleation or promotes the formation of the S phase, which belongs to the ternary Al-Cu-Mg system (see Scheil calculation in Figure 9).  To study the effect of Mg on the solidification behavior, phase field simulations with Al-2.63Cu-1.56Li-0.28Mg were performed in the identical simulation setting as before. Figure 10 presents the cooling curve and solid-fraction formation. The addition of 0.28 wt.% Mg did not significantly affect the melting temperature, nucleation temperature of the primary phase, solid fraction, and solidification range, unlike the lithium addition into Al-2.63Cu alloy. T1 temperature and fraction formation over time are presented in Figure  11a,b, respectively, showing that the nucleation temperature is not affected by magnesium addition. However, the T1 solid fraction increased slightly from 0.025% to 0.028%. To study the effect of Mg on the solidification behavior, phase field simulations with Al-2.63Cu-1.56Li-0.28Mg were performed in the identical simulation setting as before. Figure 10 presents the cooling curve and solid-fraction formation. The addition of 0.28 wt.% Mg did not significantly affect the melting temperature, nucleation temperature of the primary phase, solid fraction, and solidification range, unlike the lithium addition into Al-2.63Cu alloy. T 1 temperature and fraction formation over time are presented in Figure 11a,b, respectively, showing that the nucleation temperature is not affected by magnesium addition. However, the T 1 solid fraction increased slightly from 0.025% to 0.028%. Al-2.63Cu-1.56Li-0.28Mg were performed in the identical simulation setting as before. Figure 10 presents the cooling curve and solid-fraction formation. The addition of 0.28 wt.% Mg did not significantly affect the melting temperature, nucleation temperature of the primary phase, solid fraction, and solidification range, unlike the lithium addition into Al-2.63Cu alloy. T1 temperature and fraction formation over time are presented in Figure  11a,b, respectively, showing that the nucleation temperature is not affected by magnesium addition. However, the T1 solid fraction increased slightly from 0.025% to 0.028%.   Figure 12a). It can be seen in Figure 12b,c that when the initial composition of magnesium increased from 0.28 wt.% to 0.35 wt.%, the amount of T1 remained constant at approximately 2.87% and T1 started to appear around the same time (at 0.00686 s) during solidification. The amount of the Sʹ phase for the alloy with 0.35 wt.% magnesium (represented by the pink line in Figure 12c) was 0.1%, which is greater than that for the alloy with 0.28 wt.% magnesium. When the magnesium content was further increased up to 0.49 wt.%, it had an adverse effect on the T1 precipitation with a decrease in the T1 solid fraction, while the Sʹ phase fraction increased. Moreover, the T1 precipitation was delayed by approximately 0.0004 s compared with the alloy with 0.28 wt.% and 0.48 wt.% magnesium.  Figure 12a). It can be seen in Figure 12b,c that when the initial composition of magnesium increased from 0.28 wt.% to 0.35 wt.%, the amount of T 1 remained constant at approximately 2.87% and T 1 started to appear around the same time (at 0.00686 s) during solidification. The amount of the S phase for the alloy with 0.35 wt.% magnesium (represented by the pink line in Figure 12c) was 0.1%, which is greater than that for the alloy with 0.28 wt.% magnesium. When the magnesium content was further increased up to 0.49 wt.%, it had an adverse effect on the T 1 precipitation with a decrease in the T 1 solid fraction, while the S phase fraction increased. Moreover, the T 1 precipitation was delayed by approximately 0.0004 s compared with the alloy with 0.28 wt.% and 0.48 wt.% magnesium.

Powder Characterization by EDX Analysis
To analyze the segregation of the alloying elements (Cu and Mg) in the interdendritic regions, energy dispersive X-ray analysis (EDX) was performed. Here, EDX was used to determine the chemical composition of the material at specific points of the powder particles. Lithium, a light element, has a low energy characteristic X-ray; therefore, detecting Li in the standard EDX analysis was impossible.
The specific points for the elemental analysis for Al-2.63Cu-1.56Li-0.28Mg powder particles are represented in Figure 13. The results from the measurements of each spectrum of Al-4.5Cu and Al-2.63Cu-1.56Li-0.28Mg powder particles are given in weight percent and listed in Table 4.
According to the results from EDX point analysis, the solute concentration of both Cu and Mg was higher in the interdendritic phases, as expected from the segregation analysis (Figure 7) during phase-field simulation. In spectra 7,8,9,13, and 14, which are the points in the interdendritic regions, the measured values for Cu (in weight percent) were 14.3, 11.8, 8, 7, and 4.6, respectively. The values were comparatively higher than those measured in the primary dendritic FCC phase, whose values were represented by spectra 10, 11, and 12. Similarly, the segregation of Mg in the interdendritic phases was found to be higher compared with the FCC matrix phase.

Powder Characterization by EDX Analysis
To analyze the segregation of the alloying elements (Cu and Mg) in the interdendritic regions, energy dispersive X-ray analysis (EDX) was performed. Here, EDX was used to determine the chemical composition of the material at specific points of the powder particles. Lithium, a light element, has a low energy characteristic X-ray; therefore, detecting Li in the standard EDX analysis was impossible.
The specific points for the elemental analysis for Al-2.63Cu-1.56Li-0.28Mg powder particles are represented in Figure 13. The results from the measurements of each spectrum of Al-4.5Cu and Al-2.63Cu-1.56Li-0.28Mg powder particles are given in weight percent and listed in Table 4.
According to the results from EDX point analysis, the solute concentration of both Cu and Mg was higher in the interdendritic phases, as expected from the segregation analysis ( Figure 7) during phase-field simulation. In spectra 7, 8, 9, 13, and 14, which are the points in the interdendritic regions, the measured values for Cu (in weight percent) were 14.3, 11.8, 8, 7, and 4.6, respectively. The values were comparatively higher than those measured in the primary dendritic FCC phase, whose values were represented by spectra 10, 11, and 12. Similarly, the segregation of Mg in the interdendritic phases was found to be higher compared with the FCC matrix phase.  When comparing the results from the EDX point analysis and the segregation analysis from the phase-field simulation, it is observed that the amount of copper in the primary matrix and interdendritic region detected from the EDX point measurement was lower than that of the segregation analysis from the phase-field simulation. For instance, a maximum value of 14.3 wt.% of copper was detected in spectrum 7 in Table 4, while the copper concentration rose to 50 wt.% according to the results from phase-field simulation. We attribute this discrepancy to the limited spatial resolution of a "local" EDX point analysis. In the measurement, the concentration at a specific point is averaged over the volume where the electron beam generates the characteristic X-ray emission. For example, if the measured EDX point is focused on the interdendritic region with a higher concentration of segregated alloying elements, it will also include the FCC phase, which surrounds the interdendritic region due to the small length scale of the particle solidification microstructure. Therefore, the results from local EDX measurement are an average value over a larger volume than one captured by the results from the phase-field simulation determined by the grid spacing, which was 0.02μm in our case. It is also worth mentioning that in the phase-field simulations, concentration values were smeared over diffuse-interface regions. However, a single grid cell outside the interface has the "true" phase concentration. Hence, the effect of the diffuse interfaces can be seen in the steepness of the concentration distribution but not in the min/max values themselves (refer to Figure 7). To further confirm the explanation for the difference between EDX measurements and phasefield simulations, the simulated concentration field was mapped on different coarser grids. Figure 14 shows the sorted Cu concentration of the simulation results obtained for Al-2.63Cu-1.56Li plotted for different grid resolutions. It is evident that an evaluation on a coarser grid led to Cu concentrations that were closer to the local EDX measurement results.  When comparing the results from the EDX point analysis and the segregation analysis from the phase-field simulation, it is observed that the amount of copper in the primary matrix and interdendritic region detected from the EDX point measurement was lower than that of the segregation analysis from the phase-field simulation. For instance, a maximum value of 14.3 wt.% of copper was detected in spectrum 7 in Table 4, while the copper concentration rose to 50 wt.% according to the results from phase-field simulation. We attribute this discrepancy to the limited spatial resolution of a "local" EDX point analysis. In the measurement, the concentration at a specific point is averaged over the volume where the electron beam generates the characteristic X-ray emission. For example, if the measured EDX point is focused on the interdendritic region with a higher concentration of segregated alloying elements, it will also include the FCC phase, which surrounds the interdendritic region due to the small length scale of the particle solidification microstructure. Therefore, the results from local EDX measurement are an average value over a larger volume than one captured by the results from the phase-field simulation determined by the grid spacing, which was 0.02µm in our case. It is also worth mentioning that in the phase-field simulations, concentration values were smeared over diffuse-interface regions. However, a single grid cell outside the interface has the "true" phase concentration. Hence, the effect of the diffuse interfaces can be seen in the steepness of the concentration distribution but not in the min/max values themselves (refer to Figure 7). To further confirm the explanation for the difference between EDX measurements and phase-field simulations, the simulated concentration field was mapped on different coarser grids. Figure 14 shows the sorted Cu concentration of the simulation results obtained for Al-2.63Cu-1.56Li plotted for different grid resolutions. It is evident that an evaluation on a coarser grid led to Cu concentrations that were closer to the local EDX measurement results.  Backscattered electron (BSE) images of the gas-atomized Al-2.63Cu-1.56Li-0.28Mg powders (see Figure 16a-c) were also used in order to determine the amount of the eutectic fraction. Three measurements were carried out using three different particles of the same diameter (20 μm) with the help of the threshold feature from the ImageJ software The results from the measurement are summarized in Table 5.  Backscattered electron (BSE) images of the gas-atomized Al-2.63Cu-1.56Li-0 powders (see Figure 16a-c) were also used in order to determine the amount of the tic fraction. Three measurements were carried out using three different particles same diameter (20 μm) with the help of the threshold feature from the ImageJ sof The results from the measurement are summarized in Table 5. Backscattered electron (BSE) images of the gas-atomized Al-2.63Cu-1.56Li-0.28Mg powders (see Figure 16a-c) were also used in order to determine the amount of the eutectic fraction. Three measurements were carried out using three different particles of the same diameter (20 µm) with the help of the threshold feature from the ImageJ software. The results from the measurement are summarized in Table 5.
The total phase fraction of secondary phases in the 20 µm diameter Al-2.63Cu-1.56Li-0.28Mg particle obtained from the phase-field simulation was 2.98%, see Table 5. The secondary phases, T 1 , T B , and S , in the solidified Al-2.63Cu-1.56Li-0.28Mg droplet, could not be discriminated by EDX or image analysis, but the amount of the eutectic fraction as estimated by the threshold analysis compared well with the simulation results. As the eutectic also comprised the FCC phase, which was not counted in the mass fraction of secondary phases from the phase-field simulations, the eutectic fraction was underestimated in the simulation. A more detailed and quantitative analysis of the experimental data, together with simulation results, is subject to future work. als 2023, 16, x FOR PEER REVIEW 16 of 19 Figure 16. (a-c) Gas-atomized 20 μm Al-2.63Cu-1.56Li-0.28Mg powder in backscattered electron primary FCC phase (gray) and interdendritic phases (black); (d-f) Eutectic areas of Al-2.63Cu-1.56Li-0.28Mg powder by a threshold algorithm using ImageJ.
The total phase fraction of secondary phases in the 20 μm diameter Al-2.63Cu-1.56Li-0.28Mg particle obtained from the phase-field simulation was 2.98%, see Table 5. The secondary phases, T1, TB, and Sʹ, in the solidified Al-2.63Cu-1.56Li-0.28Mg droplet, could not be discriminated by EDX or image analysis, but the amount of the eutectic fraction as estimated by the threshold analysis compared well with the simulation results. As the eutectic also comprised the FCC phase, which was not counted in the mass fraction of secondary phases from the phase-field simulations, the eutectic fraction was underestimated in the simulation. A more detailed and quantitative analysis of the experimental data, together with simulation results, is subject to future work.

Conclusions
The solidification behavior of fast-solidifying Al-Cu-Li-Mg melt droplets during gas atomization was studied with the help of phase-field simulations using the software MI-CRESS. Previous discussions of microsegregation and phase formation during solidification of Al-Cu-Li alloys, especially T1 precipitation and eutectic fraction, are often based on the literature results obtained for conventional casting, i.e., slow solidification rates. Only a few studies were found for higher cooling rates. Reflecting on the results from the investigations conducted in this study, the following conclusions can be made: (i) The results from 2D phase-field simulations of solidifying droplets of different Al-Cu-Li-Mg alloys, radius r = 10 μm, with heat extraction rates expected for gas atomization, are consistent with experimental SEM and EDX investigations; (ii) The simulations allow a quantitative analysis of the element distribution and phase fractions of the as-solidified droplet beyond the resolution limit of the experimental SEM-EDX analysis. Other analytical methods need to be used to validate the simulation; Figure 16. (a-c) Gas-atomized 20 µm Al-2.63Cu-1.56Li-0.28Mg powder in backscattered electron primary FCC phase (gray) and interdendritic phases (black); (d-f) Eutectic areas of Al-2.63Cu-1.56Li-0.28Mg powder by a threshold algorithm using ImageJ.

Conclusions
The solidification behavior of fast-solidifying Al-Cu-Li-Mg melt droplets during gas atomization was studied with the help of phase-field simulations using the software MICRESS. Previous discussions of microsegregation and phase formation during solidification of Al-Cu-Li alloys, especially T 1 precipitation and eutectic fraction, are often based on the literature results obtained for conventional casting, i.e., slow solidification rates. Only a few studies were found for higher cooling rates. Reflecting on the results from the investigations conducted in this study, the following conclusions can be made: (i) The results from 2D phase-field simulations of solidifying droplets of different Al-Cu-Li-Mg alloys, radius r = 10 µm, with heat extraction rates expected for gas atomization, are consistent with experimental SEM and EDX investigations; (ii) The simulations allow a quantitative analysis of the element distribution and phase fractions of the as-solidified droplet beyond the resolution limit of the experimental SEM-EDX analysis. Other analytical methods need to be used to validate the simulation; (iii) In particular, for the FCC matrix phase, the amount of dissolved Li and Cu can be determined by the simulations. Moreover, the as-solidified phase fractions of θ , T 1 , T B , and S can be simulated, depending on the alloy composition. The simulation results show that: (iv) The addition of lithium to a binary Al-Cu alloy decreases the amount of dissolved copper in the primary FCC matrix; (v) The total amount of secondary phases in Al-2.63Cu-1.56Li is larger than in Al-2.63Cu, not only because of the additional alloying element lithium but also because of more copper segregating into the interdendritic regions, forming T 1 and T B precipitates together with Li; (vi) It is shown that the addition of magnesium of up to 0.35 wt.% has a significant effect on the T 1 precipitation leading to an increase in T 1 fraction. However, a further increase in magnesium content of up to 0.49 wt.% leads to a delay in T 1 formation, a decrease in T 1 fraction, and an increase in S fraction.